2x - y = 5x + 3y = 7What is the value of the system determinant?5672. One number is 7 more than twice another. If their difference is 22, what is the larger number?29  37  43

Question 1:
 For this case we have the following system of equations:
 2x - y = 5
 x + 3y = 7
 We rewrite the system of equations of the form:
 Ax = b
 Where,
 A: coefficient matrix.
 x: incognita vector
 b: vector solution.
 We have then:
 [tex]A = \left[\begin{array}{ccc}2&-1\\1&3\\\end{array}\right] b = \left[\begin{array}{ccc}5\\7\\\end{array}\right] x = \left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]
 We look for the determinant of A.
 We have then:
 [tex] A = (2) * (3) - (-1) * (1) A = 6 + 1 A = 7[/tex]
 Amswer:
 the value of the system determinant is:
 A = 7

 Question 2: 
 For this case, the first thing we must do is define variables:
 x, y: unknown numbers.
 We then have the following system of equations:
 One number is 7 more than twice another:
 [tex] y = 2x + 7 [/tex]
 their difference is 22:
 [tex] y - x = 22 [/tex] 
 Solving the system of equations we have:
 [tex] x = 15 y = 37[/tex]
 Therefore, the largest number is:
 [tex] y = 37 [/tex] 
 Answer:
 the larger number is 37